Step by step
The question
Question: find (f + g)(1) for f(x) = x² and g(x) = 3x.
f(x) = x2
g(x) = 3x
(f + g)(x) means f of x plus g of x.
We add the two answers.
(f + g)(x) = f(x) + g(x)
1 Work out f(1)
Put 1 in place of x in f.
f(1) = 12
1² means 1 times 1.
12 = 1 × 1 = 1
That is 1.
f(1) = 1
2 Work out g(1)
Put 1 in place of x in g.
We write it in brackets.
g(1) = 3(1)
3(1) = 3 × 1
3(1) means 3 times 1.
3 times 1 is 3.
g(1) = 3
3 Add them
f(1) plus g(1): 1 + 3.
(f + g)(1) = 1 + 3
So (f + g)(1) = 4.
(f + g)(1) = 4
4 Check
Let's check another way.
First the whole rule: (f + g)(x) = x² + 3x.
(f + g)(x) = x2 + 3x
Then put in 1.
We get 4 again.
It works!
(f + g)(1) = 12 + 3(1) = 1 + 3 = 4
Let's look back.
First: work out f(1).
Then: work out g(1).
Then: add them.
Last: check.
Answer
(f + g)(1) = 4